The Sig has much less felt recoil, better sights, is much quicker at fllow up shots and has a much better trigger.
The sights are better on the P238, I'll give you that, but then again, for this type pistol, they really are not needed either. I dont have any troubles making good hits with the LCP. SIG did kind of fake me out when I bought mine, as they have changed the profile of the "plain sights" (at least on the P238) to that of the usual SIG "three dot" night sights, and I thought that was what I was getting. Doom on me, I wasnt paying close enough attention I guess.
Recoil is kind of subjective, as is the trigger. I dont really see much if any difference in recoil between the two, and I have shot them side by side, same time, same ammo. At least there wasnt enough difference to draw my attention to it. The LCP's trigger is a nice DAO type trigger, but if youre not a DA shooter, you may not like it. I am a DA shooter, and dont have any problems with it. The SIG's trigger is very nice as well, and is your typical 1911 SA type trigger. Follow up shots with either are as fast as you can pull the trigger.
The P238 is a nice gun, I would just suggest if at all possible, you shoot it before you buy it. I know thats not always possible, but I would not buy another unless I could, and I'd want to put a good number of rounds through it first too. This is the first SIG I've owned, that didnt work 100% right out of the box, and these days, thats one requirement I tend to be a stickler about. I personally think "break ins" are BS.
Other than mine not being reliable, the one thing that annoys me the most, is how loud the safety is when swept off. Its as loud as my M1's, M1A's, and AK's. If I were to ever carry one, I'd probably carry it loaded with the hammer down, and just thumb cock it, as its a lot quieter, and takes about the same effort.
One thing with the Ruger, the $200+ you save in the difference in price between the two, you can buy a good bit of ammo/components to shoot with. If you can find it/them.